Using Excel Solver Company XYZ produces three models $($M$1,$ M$2,$ M$3)$ of batteries at three different locations $($plant A$,$ B$,$ C$).$ See tables below for the required production quantities for a new customer contract and the unit cost for each model. New Contract Orders Type Qty M$1240000$ M$2120000$ M$3180000$ Production Costs Type Plant A Plant B Plant C M$1$ $$0\mathrm{.}85$ $$0\mathrm{.}900\mathrm{.}65$ M$2$ $$1\mathrm{.}00$ $$1\mathrm{.}050\mathrm{.}55$ M$3$ $$1\mathrm{.}30$ $$1\mathrm{.}200\mathrm{.}6$ The combined Model $1$ & Model $2$ production capacities are $150,000$ units at Plant A and $180,000$ units at plant B and $30,000$ units at Plant C$.$ The Model $3$ production capacities are $100,000$ units at Plan A and $90,000$ units at the plant B and $40,000$ at Plant C$.$ The cost of shipping from plant A is $$0\mathrm{.}2$ per unit and from plant B is $$0\mathrm{.}25$ per unit and from Plan C $0\mathrm{.}3.$Q$2.$ Solve the linear program$\backslash$model $($setup$)$ developed in Q$1$ to determine the optimal production plan quantities.